Time is the rate at which things change, it can be measured by different kinds of clock.
Similarly there are instruments which can measure space in terms of distance.
These measurements are what they are, a mathematical proof is not required.

Time is the rate at which things change, it can be measured by different kinds of clock.
Similarly there are instruments which can measure space as length.
These measurements are what they are, a mathematical proof is not required.

Those measurements are relative though. A meter stick traveling at half the speed of light is not the same length as a meter stick sitting stationary relative to you. Same thing with a tick on a clock. Furthermore, two different observers can disagree over the timing of events. Its tough to talk about time without getting into spacetime.

Time is the rate at which things change, it can be measured by different kinds of clock.

I consider Time to be a measure of the sequence of events, or of how the rate at which regular events occur compare to other regular events. 'Proper time' is what is measured by a clock and can vary between clocks depending on gravity and relative motion. Considering Time as only what is measured by clocks ignores many complexities which can then lead to misunderstanding and 'paradoxes'. To see the full picture you have to compare the rates of time of objects in a system and have a way of translating these to determine how they behave relative to each other. That is the purpose of Special and General Relativity.